Jay McTighe and Grant Wiggins have published a paper From Common Core Standards to Curriculum: Five Big Ideas that is a distillation of their take on how best to approach the implementation of the Common Core State Standards (CCSS). They clearly point out the often fuzzy distinction between standards and curriculum. The goal in their paper is to “highlight possible misconceptions in working with the Standards, and offer recommendations for designing a coherent curriculum and assessment system for realizing their promise.”

As a fan of McTighe’s and Wiggins’ backwards design work around curriculum, assessment, and instruction, I wanted to take the time to dissect their take on the massive undertaking that is the Common Core. My focus is, thankfully, only on the Math Standards, which I refer to as CCSSM. I commend anyone who tackles the task of having a deep understanding of both the ELA and Math Standards!

This blog post is my way of making sense of their important message, so I can better internalize their message and use it in my work. This summary should not be considered a substitute for reading their paper, in which their ideas are presented in in clear, understandable prose.

Big Idea # 1 – The Common Core Standards have new emphases and require careful reading.

The authors stress the importance of looking at the standards as a whole, noticing the big overall shifts and the “goals and structure of the whole document” before zeroing in on individual grade levels. In my work with teachers and administrators in K – 12, I have witnessed this narrow focus all too often, especially with elementary teachers who teach all subjects to their students. They are faced with the arduous task of developing a deep understanding both the ELA and Math CCSS, as well as include science and social studies into their instructional mix.

An understanding of the progressions of the different math domains is important for several reasons. The CCSSM has moved some content to earlier grades than traditionally taught. In addition, focus on specific content has a distinct beginning and end in the CCSSM. For example, the study of fractions and their operations starts in Grade 3 and ends in Grade 5. Fractions are introduced in Grade 3 as points on a number line. The idea of fractions as units on the number line that can be counted (1/4, 2/4, 3/4, 4/4, 5/4, 6/4…) is introduced from the beginning, as is the connected idea that 3/4 can be thought of of three 1/4ths.

Using the idea of fractions as units of counting or measure helps students to make sense of why they can only add thirds to thirds and fifths to fifths. Students can’t add thirds to fifths because a third of a given whole and a fifth of the same given whole are not the same size. Traditionally, we have extended the study of fractions into the middle school years, and students STILL don’t get them!

This misunderstanding of units underlies students difficulties in algebra in later years. Students who don’t have a deep understanding of fractions and their operations often are are lacking the basic understanding of “unit”. Returning to the idea of adding thirds and fifths, in algebra this concept is translated to adding like or unlike terms. In K – 2, students learn that they can add oranges to oranges, but not apples to oranges. In 3 – 5, students learn that they can add thirds to thirds, but not thirds to fifths. In algebra, this same idea is translated to being able to add x’s to x’s, but not x’s to y’s. The expression 3x + 4y is written as simply as it can be expressed. This progression of the idea of units is an example of what the authors of the CCSSM call coherence. It is only through looking at the document as a whole that these streams of coherence are recognized.

McTighe and Wiggins recommend that:

…schools set the expectation and schedule the time for staff to read and discuss the Standards, beginning with the ‘front matter’ not the grade-level Standards. We also recommend that staff reading and discussion be guided by an essential question: What are the new distinctions in these Standards and what do they mean for our practice? (p. 2)

This overview will highlight the idea that the Standards for Mathematical Practice are as important, if not more important for guiding instructional changes, than the Math Content Standards. Only after understanding the overall format and expectations of the standards, do McTighe and Wiggins recommend looking at the grade level Content Standards.

I would add here that any one grade level should never be looked at in isolation. One reason is that there will always be students in any one class that are straddling the continuum of the grade level content standards. In a Grade 3 class, there will be students still struggling with Grade 2 concepts, while some of their classmates are ready for Grade 4 concepts.

For example, a Grade 4 teacher can click on K – 8 Standards, then Numbers and Operations Fractions. Grades 3, 4, and 5 will appear on the screen. One click on each Grade will list the Cluster Headings in that grade. One click on each Cluster Heading will reveal the individual standards. Another click on any of these levels will close up the level. This ability to show or hide the different levels via clicking helps tremendously when trying to understand how a concept progresses over the grade levels.

An added bonus to studying the CCSSM using Illustrative Mathematics is the inclusion of the “Illustrations”, which are tasks that illustrate a way to assess student understanding of that standard. The goal is to eventually have illustrations for each standard. The illustrations, some of which are developed by classroom teachers, are juried by the Institute for Mathematics and Education to ensure quality and alignment with the CCSSM.

McTighe and Wiggins conclude their first Big Idea of closely reading the standards as a whole by saying:

We cannot overemphasize the value of taking the time to collaboratively examine the Standards in this way. Failure to understand the Standards and adjust practices accordingly will likely result in “same old, same old” teaching with only superficial connections to the grade level Standards. In that case, their promise to enhance student performance will not be realized. (p. 2)

Big Idea # 2 – Standards are not curriculum.

The distinction between standards and curriculum is a slippery one that is not easily understood. McTighe and Wiggins compare the relationship of the curriculum to the standards using the metaphor of the curriculum as a “house” and the standards as the “building code”.

Architects and builders must attend to them but they are not the purpose of the design. The house to be built or renovated is designed to meet the needs of the client in a functional and pleasing manner – while also meeting the building code along the way. (p. 3)

The standards are the end product of what students need to understand and be able to do with the content. They do not attempt to tell teachers how to teach the content. Teaching is an art. There is no one method that fits all teachers or all students.

So how do the authors define curriculum? McTighe and Wiggins state that when they were researching for their book Understanding by Design® (Wiggins and McTighe, 1998), “we uncovered 83 different definitions or connotations for the word, curriculum, in the educational literature! ” No wonder the distinction between standards and curriculum is so slippery. Most of the definitions that the authors found for curriculum “focus[ed] on inputs, not outputs – what will be ‘covered’ rather than a plan for what learners should be able to accomplish with learned content. This is a core misunderstanding in our field.”

The authors close this Big Idea with the warning: “Marching through a list of topics or skills cannot be a ‘guaranteed and viable’ way to ever yield the sophisticated outcomes that the Standards envision.” (p.4)

Big Idea # 3 – Standards need to be “unpacked.”

I have to admit that I have always cringed at the phrase “unpacking the standards”, so I am going into this big idea with a bias. The phrase always engenders an image of opening a suitcase and putting this in one drawer and that in another drawer and hanging that up. What this in turn conjures up is that, although these are all necessary, they have different uses and needs for long term storage and we only pack them together when we have to for expediency. As I read more of this big idea, perhaps I’m being a bit harsh on “unpacking”. Maybe it’s just that I have heard the phrase thrown around so much as a catch-phrase for all things standards-based, making is sound like one just has to sit down and DO it, and then it will be done. Okay, we’ve unpacked! Now we’re done! The key is that we still have to remember where we put everything and use it as it is designed to be used.

Here are the four “drawers” (categories) that McTighe and Wiggins recommend be used when unpacking:

1) Long term Transfer Goals

2) Overarching Understandings

3) Overarching Essential Questions

4) A set of recurring Cornerstone Tasks.

Transfer goals refer to what we want students to be able to do in the long term. In math, we want students to be creative problem solvers, able to creatively apply relevant content skills and habits of mind (practice standards) to work through problem situations that they may not have ever seen before. We want them to internalize these skills, applying them to solving problems making them part of how they approach problem solving for the rest of their lives., not just until the end of the course.

The authors suggest that the next two categories, Overarching Understandings and Essentials Questions can be viewed as two sides of the same coin:

The Understandings state what skilled performers will need in order to effectively transfer their learning to new situations, while explorations of the Essential Questions engage learners in making meaning and deepening their understanding. (p. 4-5)

An example provided by the authors to show the different sides of the coin is Mathematical Modeling, which is one of the Standards for Mathematical Practice, as well as an individual Domain in the HS CCSSM.

Overarching Understandings

• Mathematicians create models to interpret and predict the behavior of real world phenomena.

• Mathematical models have limits and sometimes they distort or misrepresent.

Overarching Essential Questions

• How can we best model this (real world phenomena)?

• What are the limits of this model?

• How reliable are its predictions?

The Cornerstone Tasks are designed to bring the other three categories together. McTighe and Wiggins have defined Cornerstone Tasks as assessment tasks that are “like the game in athletics or the play in theater, teachers teach toward these tasks without apology.” Too often, I hear the phrase “teaching to the test” used with disdain. My opinion is that if the “test” is truly testing what we want students to know and be able to do, why should we not teach to it? It is yet to be seen if SBAC and PARCC can effectively assess the essence of the CCSSM. However, I really don’t care about those “tests” (said in a hushed voice). I care about students being given authentic problem solving experiences on a regular basis throughout their school career. In my opinion, the “test” is can the students use what they have learned to solve real life problems and become productive adults?

McTighe and Wiggins sum up Cornerstone Tasks in this way:

Cornerstone tasks are designed to recur across the grades, progressing from simpler to more sophisticated; from those that are heavily scaffolded toward ones requiring autonomous performance. Accordingly, they enable both educators and learners to track performance and document the fact that students are getting progressively better at using content knowledge and skills in worthy performances. (p. 6)

Concluding their “unpacking” Big Idea, the authors warn against only unpacking on a “micro level”. They include a cautionary note from the Kansas Department of Education, which concludes with:

Metaphorically speaking, ‘unpacking’ often leads educators to concentrate on the trees at the expense of the forest. (p. 6)

They include a quote directly taken from the CCSSM in its introduction of the Practice Standards:

“The Standards for Mathematical Practice describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle and high school years. Designers of curricula, assessments, and professional development should all attend to the need to connect the mathematical practices to mathematical content in mathematics instruction.” (p. 7)

In this Big Idea, the authors keep the discussion focused on the learner rather than on the content.

Thus, the first question for curriculum writers is not: What will we teach and when should we teach it? Rather the initial question for curriculum development must be goal focused: Having learned key content, what will students be able to do with it? (p. 7)

Included in this Big Idea is a succinct way to clarify what is meant by “college and career readiness”.

Our long-standing contention applies unequivocally to the Common Core Standards as well as to other Standards: The ultimate aim of a curriculum is independent transfer; i.e., for students to be able to employ their learning, autonomously and thoughtfully, to varied complex situations, inside and outside of school. Lacking the capacity to independently apply their learning, a student will be neither college nor workplace ready. (p. 7)

McTigue and Wiggins warn against the temptation to list individual content standards on a calendar, focusing on “coverage” while ignoring the importance of students gradually transferring increasingly complex content and practice skills in order to solve non-routine problems.

The authors discuss the misconception that the Standards “prescribe the instructional sequence and pacing.” They include another quote directly from the CCSSM that speaks to this misconception:

“For example, just because topic A appears before topic B in the standards for a given grade, it does not necessarily mean that topic A must be taught before topic B. A teacher might prefer to teach topic B before topic A, or might choose to highlight connections by teaching topic A and topic B at the same time. Or, a teacher might prefer to teach a topic of his or her own choosing that leads, as a byproduct, to students reaching the standards for topics A and B.” (p. 8)

Finally, after the authors include an apt parallel between the training of soccer players to the teaching of students, they conclude with a paragraph that reads much better on its own than any summary I could write:

To design a school curriculum backward from the goal of autonomous transfer requires a deliberate and transparent plan for helping the student rely less and less on teacher hand-holding and scaffolds. After all, transfer is about independent performance in context. You can only be said to have fully understood and applied your learning if you can do it without someone telling you what to do. In the real world, no teacher is there to direct and remind you about which lesson to plug in here or what strategy fits there; transfer is about intelligently and effectively drawing from your repertoire, independently, to handle new situations on your own. Accordingly, we should see an increase, by design, in problem- and project-based learning, small-group inquiries, Socratic Seminars, and independent studies as learners progress through the curriculum across the grades. (p. 9)

Big Idea #5 – The Standards come to life through the assessments.

McTighe and Wiggins revisit several themes in this section, such as the importance of output rather than input, the metaphor of assessments as games or performances, and backwards design:

The curriculum and related instruction must be designed backward from an analysis of standards-based assessments; i.e., worthy performance tasks anchored by rigorous rubrics and annotated work samples. We predict that the alternative – a curriculum mapped in a typical scope and sequence based on grade-level content specifications – will encourage a curriculum of disconnected “coverage” and make it more likely that people will simply retrofit the new language to the old way of doing business. (p. 11)

The authors warn against thinking of the Grade Level standards as discrete statements that need to be assessed separately. “This confuses means and ends; it conflates the ‘drill’ with the ‘game.’ Assessments should instead be designed to encompass as set of connected content standards and the practice standards.”

McTighe and Wiggins have done a fine job of tying the CCSSM to their backwards design process. Their synthesis of the CCSSM to five key ideas gives me a framework with which to talk to teachers, principals and curriculum coordinators as I work with them to help them roll out the CCSSM in their schools. I have a feeling that the authors have a book is in the works that would serve as a foundational resource as educational practitioners approach this big sea change.